Inference on the Effects of Observed Features in Latent Space Models for Networks

Abstract

The latent space model (LSM) for network data is a generative probabilistic model that combines a generalized linear model with a latent spatial embedding of the network. It has been used to decrease error in the estimation of and inference regarding the effects of observed covariates. In applications of the LSM, it is assumed that the latent spatial embedding can control for unmeasured confounding structure that is related to the values of edges in the network. As far as we know, there has been no research that considers the LSM’s performance in adjusting for unmeasured structure to reduce estimation and inferential errors. We investigate the LSM’s performance via a Monte Carlo study. In the presence of an unmeasured covariate that can be appropriately modeled using a latent space, estimation and inferential error remain high under even moderate confounding. However, the prediction error of the LSM when unmeasured network structure is present is substantially lower in most cases. We conclude that the LSM is most appropriately used for exploratory or predictive tasks.